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Math Help - metric space

  1. #1
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    metric space

    Hi , i have this problem , i need help with this exercise


    If b \notin B[a,r] , prove that exist s>0 such that B[a,r] \cap B[b,s] = \emptyset


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  2. #2
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    Re: metric space

    Quote Originally Posted by resident911 View Post
    Hi , i have this problem , i need help with this exercise
    If b \notin B[a,r] , prove that exist s>0 such that B[a,r] \cap B[b,s] = \emptyset
    Please, please get in the habit of posting the meaning of notations that you use.
    If B[a,r]=\{x:d(a,x)<r\} the ordinary ball then the statement is false.
    If B[a,r]=\{x:d(a,x)\le r\} the ordinary closed ball then the statement is true.
    Which is it? Or is it something altogether different?
    Thanks from emakarov
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